Irish theatre in a London 'Wood'! (5)

I believe the answer is:

abbey

I'm a little stuck... Click here to teach me more about this clue!

'irish theatre' is the definition.
'abbey' can be an answer for 'theatre' (I've seen this before). I am not sure about the 'irish' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for abbey that I've seen before include "Religious building" , "sacred place" , "Religious establishment" , "theatre" , "Religious house" .)

I've seen this clue in the Evening Standard.

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